Search for Rare Decays of Ds+ to Final States π+e+e-, ρ+e+e-, π+π0e+e-, K+π0e+e-, and KS0 π+e+e-

Using 7.33 fb-1 of e+e-collision data collected by the BESIII detector at center-of-mass energies in the range of s=4.128-4.226 GeV, we search for the rare decays Ds+→h+(h0)e+e-, where h represents a kaon or pion. By requiring the e+e-invariant mass to be consistent with a φ(1020), 0.98<M(e+e-)<1.04 GeV/c2, the decay Ds+→π+φ, φ→e+e-is observed with a statistical significance of 7.8σ, and evidence for the decay Ds+→ρ+φ, φ→e+e-is found for the first time with a statistical significance of 4.4σ. The decay branching fractions are measured to be B(Ds+→π+φ,φ→e+e-)=(1.17-0.21+0.23±0.03)×10-5, and B(Ds+→ρ+φ,φ→e+e-)=(2.44-0.62+0.67±0.16)×10-5, where the first uncertainties are statistical and the second systematic. No significant signals for the three four-body decays of Ds+→π+π0e+e-, Ds+→K+π0e+e-, and Ds+→KS0π+e+e-are observed. For Ds+→π+π0e+e-, the φ mass region is vetoed to minimize the long-distance effects. The 90% confidence level upper limits set on the branching fractions of these decays are in the range of (7.0-8.1)×10-5.